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Physical Review A

Spectral properties of light in quantum optics

L. Knöll, W. Vogel, D.‐G. Welsch

Published Jul 1, 1990• 60 citations
Publisher

Abstract

The problem of spectral filtering of quantized light fields is studied, based on the recently developed quantum-optical theory of the action of passive, lossless optical systems [L. Kn\"oll, W. Vogel, and D.-G. Welsch, Phys. Rev. A 36, 3803 (1987)]. Expressions for the operator of the electric field strength of the light and the normally and time-ordered field-correlation functions are derived for the case of a Fabry-P\'erot interferometer being present. Various kinds of field decomposition that are usually considered in classical optics are studied. The results are compared with the Fourier approach to spectral properties of light. It is shown that, dependent on the experimental scheme used, new quantum effects appear, which may prevent the observation of the Fourier structure of the light as predicted from classical optics. Quantitatively this is demonstrated for the example of spectral squeezing in resonance fluorescence, where significant discrepancies between the measured and the full Fourier spectrum are found.

DOI
10.1103/physreva.42.503

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The problem of spectral filtering of quantized light fields is studied, based on the recently developed quantum-optical theory of the action of passive, lossless optical systems [L. Kn"oll, W. Vogel, and D.-G. Welsch, Phys. Rev. A 36, 3803 (1987)]. Expressions for the operator of the electric field strength of the light and the normally and time-ordered field-correlation functions are derived for the case of a Fabry-P'erot interferometer being present. Various kinds of field decomposition that are usually considered in classical optics are studied. The results are compared with the Fourier approach to spectral properties of light. It is shown that, dependent on the experimental scheme used, new quantum effects appear, which may prevent the observation of the Fourier structure of the light as predicted from classical optics. Quantitatively this is demonstrated for the example of spectral squeezing in resonance fluorescence, where significant discrepancies between the measured and the full Fourier spectrum are found.
Based on the measurement of quantum correlation functions, the quantum statistical properties of spectral measurements are studied for broadband radiation fields. The spectral filtering of light before its detection is compared with the direct detection followed by the spectral analysis of the recorded photocurrents. As an example, the squeezing spectra of the atomic resonance fluorescence are studied for both types of filtering procedures. The conditions for which the detection of the nonclassical signatures of the radiation is possible are analyzed. For the considered example, photocurrent filtering appears to be the superior option to detect nonclassicality due to the vacuum-noise effects in the optical filtering.
A theoretical investigation of spectrally filtered broadband light fields is undertaken. More specifically, the balanced homodyne correlation measurement scheme is extended using spectral filters. The technique provides a way to spectrally resolve correlation functions, making it possible to measure the squeezing spectrum. Two-level resonance fluorescence is included as a concrete example of this, providing some predictions concerning the parameters of the setup for potential experiments. Furthermore, spectral filtering is compared to electronically filtering the current generated in the photodetectors. This is of interest since filtering the current is a classical operation, whereas having optical filters in the path of the radiation is a quantum one.
A quantum optical formulation of the action of passive, lossless optical instruments on quantum light fields is developed. The quantum Maxwell equations are formally solved and the commutation relations for various combinations of field operators at different times are studied. General relationships between field correlation functions and correlation functions of source-quantity operators and free-field operators are derived. Formulas are presented for the case when the free field is the vacuum field. Furthermore, the mixing of source-field light with coherent free-field light is treated. The theory is applied to the calculation of the photocount distribution. The theory presented renders it possible to take into account the effects of light propagation through the optical system. It is shown that the effect of the optical instruments may be taken into account by introducing an apparatus function in a way which formally corresponds to that of classical optics. However, the calculation of the corresponding convolution integrals is governed by operator ordering rules, which are essential in the case of quantum light fields and which can give rise to substantial differences between classical and quantum optics.
The theory of the intensity correlations between photons of different frequencies is re-examined from basic principles and is found to lead to an expression for the correlation function containing operator products which are normally ordered in time. This expression leads to results which are free of certain extra contributions that arise in another version of this theory which contains non-normally ordered products. The analysis presented is based on a description of the frequency-filtering process in terms of Fabry-Perot interferometers. The mirrors of the interferometers are modelled as classical dielectrics. The EM field in the presence of these dielectrics is then quantised and the intensity correlation function defined in terms of these modified field operators. The results are examined in detail for the case of a light field radiated by a two-level atom.